Fourier transform-second-harmonic generation imaging is employed to obtain quantitative metrics of collagen fibers in biological tissues. In particular, the preferred orientation and maximum spatial frequency of collagen fibers for selected regions of interest in porcine trachea, ear, and cornea are determined. These metrics remain consistent when applied to collagen fibers in the ear, which can be expected from observation. Collagen fibers in the trachea are more random with large standard deviations in orientation, and large variations in maximum spatial frequency. In addition, these metrics are used to investigate structural changes through a 3D stack of the cornea. This technique can be used as a quantitative marker to assess the structure of collagen fibers that may change due to damage from disease or physical injury.
© 2009 Optical Society of America
Collagens are a family of fibrous proteins found in all multicellular animals, and account for 25% of the total protein mass in mammals . Collagen molecules organize into hierarchical fibrillar structures that form fiber bundles which display a high degree of spatial organization. These fibers can be found in the cornea, bone, cartilage, and skin [1–5]. Connective tissue diseases such as osteogenesis imperfecta and Ehlers-Danlos Syndrome are known to alter the organization of collagen fibers [6, 7]. Therefore, monitoring the structure of fibrillar collagen is quintessential for understanding its function in tissues. Within the past decade, second-harmonic generation (SHG) microscopy has become an increasingly popular technique for achieving this [8–17].
SHG microscopy has been extensively used in medicine and biology to obtain images of highly-ordered structures such as collagen fibers, microtubulin, and skeletal muscle, with high resolution and contrast [8–17]. This form of nonlinear optical microscopy results from coherent second-order nonlinear scattering wherein a noncentrosymmetric structure emits light at half the wavelength of the incident (pump) optical field. Collagen fibers, being intrinsically noncentrosymmetric, emit SHG, and thus produce high-contrast images using this technique, without the need for staining. Notwithstanding the impressive advances in SHG imaging, most studies in the past have relied on the qualitative assessment of obtained images for analysis [12, 13, 18]. Recently, researchers have made major strides in developing quantitative metrics for this imaging modality [9, 14–16, 19].
Although there are several recent approaches to quantitative SHG imaging, we briefly discuss a few. One approach uses forward-to-backward (F/B) ratio of the emitted SHG signal to reveal additional information about the environment of collagen fibers . It was found that solutions (NaCl) of high ionic strength reduced the F/B ratio for adult tendons, and was attributed to sub-diffraction structural changes in collagen fibers. In another study, the F/B ratio was used to differentiate between types of collagen . Type I collagen which is highly crystalline produces strong a F/B SHG signal, while Type III and IV collagen which are less crystalline produces a weaker signal. Yet another metric is the relative components of the second-order nonlinear susceptibility tensor . These elements are extracted from the SHG images in order to determine the orientation angle of myosin and collagen harmonophores in gastrocnemius muscle and tendon. Recently, these elements were obtained at the pixel level to differentiate between different SHG generators within the human dermis and the collagen-muscle junction of a chicken wing . Another measure is the distribution of length of structures in a tissue . In particular the SHG signal emitted from the myosin filaments of sarcomeres, were quantified by length distribution to investigate the mice and human skeletal muscle tissue. It was thus possible to examine the disease stage, recovery, and aging of the muscle tissues. In addition to these approaches, Fourier analysis could be used to derive quantitative markers for assessment of biological structures . Very recently, along with other parameters, the geometric distribution of spatial frequencies in the 2D Fourier transform (FT) was used to quantify the disorganization of collagen fibers due to photo-thermal damage in porcine corneas. It was found that regularity in fiber organization leads to an elliptical FT distribution whereas randomness leads to a more circular distribution. Aside from this work, to our knowledge, Fourier analysis has yet to be fully utilized in SHG imaging as a means of deriving quantitative measures for biological structures. In this paper, we propose the use of Fourier transform-SHG (FT-SHG) microscopy to obtain information on collagen fiber orientation and maximum spatial frequency in an image. Such a tool could aid in identifying parameters that represent the organization of collagen fibers, which could lead to the development of quantitative biomarkers help discriminate between healthy and damaged tissues.
We use FT-SHG microscopy to identify two parameters: “preferred” orientation and maximum spatial frequency. Selected regions of interest are considered for analysis of SHG images of collagen fibers in porcine trachea, ear, and cornea. The FT-SHG method is applied to 2D images as well as a 3D image stack of the cornea.
The FT is an essential mathematical tool that has been used in a variety of fields to analyze the frequency content of acquired signals and is typically carried out in 1D . The technique can be applied to images through the use of the 2D FT, whereby image contents are decomposed into a superposition of harmonic functions (of varying amplitudes and phases) along horizontal and vertical axes [21–23]. The associated spatial frequencies are simply the modulations in intensity in the image per unit distance [24, 25]. Lower frequencies are closer to the origin (point at which spatial frequency is zero), while higher frequencies are further away. The thickness and spacing of a 1D periodic structure can be determined via the spectrum in Fourier space. For an aperiodic structure, the Fourier transform is more complex, making it more challenging to extract information about features in real space. In reality, our images of biological systems are between these two extremes, and often data analysis is complicated by noise due to the scattering of the photons used to acquire the image. This limits the spatial resolution that could be obtained in optical microscopy to less than the theoretical value, and hence the fidelity with which the maximum spatial frequency can be determined in Fourier space [24–26]. This maximum spatial frequency informs us about the minimum observable size (or feature) in real space. In our approach, we extract a maximum spatial frequency, Fhigh, above the noise floor. We first determine Fhigh by extracting a line spectrum from a 2D FT along the direction of interest. Then, a smoothing spline is applied to the profile using the curve fitting toolbox in Matlab. Finally, in order to mitigate the unwanted contributions of (photon) noise to our spectrum, we use a threshold of 10% above the noise floor, which is chosen from the FT of an area that clearly produces no SHG signal (black areas in images). Using this method, the threshold is determined for each specimen. The frequency at which the amplitude just reaches above the threshold is selected as Fhigh. This approach is common for noise removal in Fourier analysis [19, 27].
The second parameter that we extract from the Fourier space is preferred orientation. Improved accuracy in Fourier space is often used to determine the orientation of an image in real space . When structures in an image have a preferred orientation, the high amplitudes on average align along a direction perpendicular to the preferred orientation in the 2D FT. Although there are other methods to obtain the orientation of structures, we employ a simple procedure that does not invoke the use of complex algorithms nor polarization modulation techniques [29–31]. In our approach, a binary image is created by isolating dominant spatial frequencies (highest amplitudes) using a desired amplitude threshold. The isolated frequencies are assigned an amplitude of 1, and all other frequencies are given an amplitude of zero. Finally, a best-fit line is applied to this binary image, which is along a direction that is perpendicular to the preferred orientation. The standard deviation in orientation is the standard error in fitting a line.
3.1 Sample preparation
Porcine tissue samples of hyaline and elastic cartilage from the trachea and ear, respectively, and cornea were harvested from a local abattoir just after euthanasia, and stored in 10% formalin. The samples were then processed for 24 hrs using a standard xylene/ethanol gradient series. The samples were then embedded in paraffin wax, and 5-µm thick sections were cut with a microtome and mounted onto glass slides using a permanent mounting media.
3.2 Experimental setup
The schematic of the experimental setup for the SHG microscope is shown in Fig. 1. An epiconfiguration two-photon fluorescence microscope is modified into a trans-configuration SHG microscope. The beam is obtained from a tunable Ti:Sapphire laser (Spectra-Physics Tsunami) that produces 100 femtosecond-duration pulses at 80 MHz repetition rate. The pulses are linearly polarized and spectrally centered at 800 nm for the experiments reported here. The beam is spatially filtered and collimated before sending it to the galvanometer based xy scanner (Cambridge Technology) which is driven in a raster-scan pattern. After passing through a combination of relay lenses (scan and tube lens), the beam is reflected by a short-pass 680-nm dichroic beam splitter (Semrock FF670-SDi01-25X36) and subsequently focused onto the sample using an oil-immersion objective (Leica 63X HCXPLAPO). The transmitted signal from the sample is collected by a second objective (Leica 20X HCPLAPOCS). Spectral detection of the SHG signal is achieved by using a laser blocking filter (Semrock FF01-680/SP-25) followed by a 390/20 nm bandpass filter (Semrock FF01-390/18-25), and the SHG intensity is recorded with a photo-multiplier tube (Hamamatsu). Image stacks are acquired from various depths (z) into the sample at a rate of ~ one frame per second. The scan area for the trachea and ear is 163×163 µm, and 238×238 µm for the cornea. An average power of 37 mW is used on the cartilage samples, and 25 mW on the cornea. These power settings are chosen for optimum image contrast.
4. Results and Discussion
4.1 SHG Microscopy of Trachea, Ear, and Cornea
Figure 2 shows SHG images of unstained slices of adult porcine trachea (2a), ear (2b), and cornea (2c). It is observed from Fig. 2a that the matrix in trachea is that of collagen fibers with elliptical gaps. This is the expected structure of hyaline cartilage . The image of the ear shows rope-like regularly oriented collagen fibers as shown in Fig. 2b. However, the cornea contains patches of collagen fibers with varying density and orientation. SHG imaging of human cornea has previously been reported [18, 19] and shows similar features to those observed in Fig. 2c. The optical sectioning capability of SHG microscopy is observed in the movie in Fig. 2d, where a 3D rendering of fibers in ear is shown.
4.2 Preferred orientation
To estimate the preferred orientation, selected regions of the collagen fibers in porcine ear and trachea are considered as shown in Figs. 3a and 3b. Their respective 2D FT after being converted to binary images are shown in Fig. 3c. For the ear, the estimated preferred orientations for the three regions are 71.3°, 69.0°, and 69.4°, respectively. This is consistent across the regions of interest to within ~5°. The standard deviation (SD) is an indicator of the number of fibers that deviate from the preferred orientation. Thus, the standard deviation is higher for randomly oriented features. It is observed that the fibers are more random in region 3 (SD=4°) compared to those in region 2 (SD=1.6°).
For the trachea, the preferred orientation in regions 4 and 5 are 45.5° and 51.8°, respectively, while the orientation in region 6 is completely different with a value of 108°. The standard deviations are larger for trachea (on average) compared to those obtained for the ear, indicating that the collagen fibers are more randomly organized in the trachea.
4.3 Maximum spatial frequency of biological tissues
Maximum spatial frequencies are obtained by dividing the SHG images of porcine ear and trachea cartilage into horizontal rectangular regions of interest (for representation, we only show one) as shown in Figs. 4a and 4b, respectively. Since the preferred orientation of the ear is relatively consistent at 70° as shown in Fig. 3c, we rotate the image of the ear by 20° so that the fibers are oriented preferentially along the vertical axis. This allows us to access the spatial frequencies along the direction of maximum variation which, in this case, is along the horizontal direction. With regards to the trachea, since the orientation varies from at least 45° to 108°, we are free to apply the same window of observation used on the ear, but without the need for any rotation of the image.
Histograms of the values of Fhigh from all regions of interest of the ear and trachea are shown in Fig. 4c and 4d, respectively. Overall, the image of the ear (Fig. 4a), as observed in real space (space domain), shows consistency in its structure. This is confirmed by the narrow distribution of the values of Fhigh as shown in the histogram (Fig. 4c), where the values for Fhigh remain between 0.51 and 0.79 µm-1. In contrast, changes in the structure of the trachea (Fig. 4b) are clearly observed in the space domain across various regions, which are confirmed by the wider distribution in the values of Fhigh as shown in the Fig. 4d. Here, Fhigh varies from 0.34 and 1.47 µm-1. This indicates that the size of the smallest feature in the trachea changes more in comparison to the ear. The error in all values of Fhigh is 0.006 µm-1, which corresponds to the separation between data points in the discrete Fourier domain.
4.4 Image stack of the Cornea
Figure 5 shows the regions of interest 1–3 for a slice in the image stack of the cornea. Region 1 has a relatively large standard deviation (6.1°) due to the random orientation of its fibers. It also has lower Fhigh (0.69 µm-1) indicating that the smallest feature size is ~1.45 µm. However, regions 2 and 3 have regularly oriented fibers and thus have low standard deviations (~1.5°). In these regions, the values of Fhigh are relatively large (~1.02 µm-1), corresponding to smallest feature size in each region of ~0.98 µm. Thus, regions 2 and 3 have comparatively thinner and closer spaced features than those in region 1.
Until now, we have determined the preferred orientation and highest spatial frequency in a plane for 2D images. Next, we extend the technique to 3D by using an image stack of the porcine cornea (3-µm thick specimen). The variations in the calculated preferred orientation and Fhigh versus depth, for the three regions in the image stack are shown in the Fig. 6. A movie of the variations in the two quantitative parameters, preferred orientation and F high versus depth for three regions of interest in the 3D image stack is shown in the Fig. 6a. The arrows represent the preferred orientation of the regions, and the color of the border for each region of interest corresponds to a value of Fhigh as indicated by the color bar.
For region 1, the preferred orientation appears to oscillate about 120°. The standard deviation in orientation remains relatively large (4.9° to 7.8°). This indicates that the fibers in region 1 are more randomly oriented throughout the stack. The values of Fhigh are relatively small. The average value of Fhigh throughout the depth is 0.77 µm-1, which corresponds to a minimum feature size of 1.3 µm.
In the case of region 2, the preferred orientation decreases from 37° to 27° over a depth of 0.49 µm. It then remains constant over a depth of 1.47 µm and then increases gradually to 37° at the end of the stack. Fhigh ranges from 0.73 to 1.50 µm-1. It increases initially and then stays roughly the same (1.27 µm-1) before it decreases to 0.80 µm-1 at the end of the stack. As can be seen from Fig. 5, region 2 has more regularly oriented structures, and thus the standard deviations in orientation are smaller compared to those obtained for region 1.
For region 3, we observe that the preferred orientation remains consistent at ~125° throughout the stack. However, Fhigh initially decreases from 0.77 to 0.44 µm-1 over a depth of 0.33µm and then gradually increases until the end of the stack. This indicates that fibers become more closely packed yet maintain the same orientation. For example, the minimum feature size decreases from 2.27 µm (at a depth of 0.33 µm) to 0.79 µm (at a depth of 2.77 µm), while the orientation stays at ~122° without deviating by more than 5°. Moreover, the standard deviation in orientation decreases at the end of the stack indicating that fibers become more regular.
We note that the size of the box chosen for estimating the preferred orientation and spatial frequency is not arbitrary. It should be chosen in such a way that it is not so small that it probes too few fibers leading to possible errors in the calculation of preferred orientation, such as those arising from a reduced number of pixels used in the FT.
We demonstrated the use of Fourier transform-second-harmonic generation (FT-SHG) imaging of collagen fibers as a means of performing quantitative analysis of obtained images. FT-SHG was applied to selected spatial regions in SHG images of collagen fibers in porcine trachea, ear, and cornea. Two quantitative markers, preferred orientation and maximum spatial frequency, Fhigh, were proposed for differentiating structural information between various spatial regions of interest in the specimens. The ear showed consistent maximum spatial frequency and orientation both in its real-space image as well as with respect to the obtained parameters. However, there were observable changes in the orientation and minimum feature size of fibers in the trachea which were quantified using our proposed parameters. Finally, the analysis was applied a 3D image stack of the cornea. It was observed that the standard deviation of the orientation was sensitive to the variation in fiber orientation and that Fhigh was sensitive to the minimum feature size. Regions that had variations in Fhigh while orientation remained relatively constant, suggested that this parameter is useful as an independent marker for characterizing changes in fiber structure. We emphasize that FT-SHG is a simple, yet powerful, tool for extracting information from images that is not obvious in real space.
Future work with FT-SHG includes quantification of the structural changes in collagen fibers due to damage from disease or injury. This could lead to developing standards essential for diagnostic applications. Here, FT-SHG is applied on the trachea, ear, and cornea, however, it can also be applied to others tissues containing fibrillar collagen such as artery walls, and include other noncentrosymmetric structures such as myosin.
This work was supported by the University of Illinois at Urbana-Champaign (UIUC) research start-up funds. M. R. M. acknowledges support from the National Science Foundation (DBI 0839113). We are grateful for the useful discussions we have had with Brynmor Davis and Kaspar Ko. We thank Duohai Pan and Jon Ekman for use of the microscope facilities, training and assistance at the Beckman Institute, UIUC. We appreciate the help of Larry Schook and Laurie Rund for providing the samples, and Donna Epps for sample preparation.
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